Steady-states for shear flows of a liquid-crystal model: Multiplicity, stability, and hysteresis |
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Authors: | Tim Dorn Weishi Liu |
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Institution: | a Department of Mathematics & Computer Science, North Georgia College & State University, Dahlonega, GA 30597, United States b Department of Mathematics, University of Kansas, Lawrence, KS 66045, United States |
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Abstract: | In this work, we study shear flows of a fluid layer between two solid blocks via a liquid-crystal type model proposed in C.H.A. Cheng, L.H. Kellogg, S. Shkoller, D.L. Turcotte, A liquid-crystal model for friction, Proc. Natl. Acad. Sci. USA 21 (2007) 1-5] for an understanding of frictions. A characterization on the existence and multiplicity of steady-states is provided. Stability issue of the steady-states is examined mainly focusing on bifurcations of zero eigenvalues. The stability result suggests that this simple model exhibits hysteresis, and it is supported by a numerical simulation. |
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